Scientific Lectures

We investigate the problem of computing an evolution scenario based on
genome rearrangements between two genomes modelized by synteny blocks,
or in mathematical terms, sorting signed permutations by reversals. We
consider the case of scenarios tha&nbsp more››

The oldest competition for an optimal shape (area-maximizing) was won by the circle. We want to give the thousandth proof !
Then we measure the perimeter in different ways, which changes the
problem (and has applications in medical i&nbsp more››

The prototype problem is the behavior at infinity of all solutions of a
linear elliptic equation that have finite L1 norm in a half cylinder
0<y, x in D,D a smoothly bounded domain. We assume that the
coefficients of the elliptic operator,as we&nbsp more››

This talk explores some of the issues that arise in statistical
modeling of atmospheric phenomena on a global scale, using total column
ozone as measured by the satellite-based Total Ozone Mapping
Spectrometer (TOMS) as a case study. A basic issue&nbsp more››

Let S be a linear space of vector valued functions u(y) on the
half-line whose values belong to some Banach space. We suppose that S
is translation invariant; that is, if u(y) belongs to S, so does u(y+t)
for all t>0. S is called 'interior comp&nbsp more››

For many questions in explicit arithmetic geometry of curves,
one needs detailed information on the rational points of the Jacobian
of the curve. A first step is to bound the free rank of the finitely
generated group that they form. For hyperellip&nbsp more››

The problem of streaming data has gained importance in recent years
because of advances in hardware technology. The ubiquitous presence of
data streams in a number of practical domains has generated a lot of
research in this area. Example applicat&nbsp more››

In a market consisting of a money market and one stock with
price process dS(t)=S(t)[a(t) dt + b dW(t) + g dM(t)] where W is a
Wiener process and M is a compensated Poisson process, an agent invests
his initial wealth in a portfolio to maxim&nbsp more››

Zeta functions and L-functions contain arithmetic information when evaluated at special values, such as s = 0. In the 1970s, Stark conjectured that the derivatives of L-functions at s = 0 can be evaluated by certain algebraic units. Under certain cir&nbsp more››

We construct a translation-invariant matching between vertices of
different labels of Bernoulli(1/2) percolation on Z^d, in such a way
that the probability that a vertex is at distance > r from its pair
decays as an exponential function of the&nbsp more››

Candes, Romberg and Tao recently studied problems of approximate and
exact reconstruction of sparse signals from incomplete random
measurements and related them to the eigenvalue behavior of submatrices
of matrices of random measurements. In parti&nbsp more››

Statistical theory is often categorized as either "Bayesian" or
"frequentist", and statisticians often self-identify in the same
categories. During the development of theoretical statistics as a
separate field in the twentieth&nbsp more››

The algebraic centre of the uniformly continuous compactification GUC of an abelian locally compact group G is G itself. There is a stronger result: if u commutes with just two (carefully chosen) elements of&nbsp more››

William Thurston conjectured over twenty years ago that every compact
hyperbolic 3-manifold whose boundary is a possibly empty union of tori
is virtually fibred, that is, has a finite cover which fibres over the
circle. If true, it provides a sign&nbsp more››

The natural link between mathematics and ecology is evident in the
field of physical ecology, which uses physical models to explore some
fundamental issues. These include how aquatic organisms use the
constraints imposed by physical environment to&nbsp more››

We state conditions for existence and uniqueness of equilibria in
evolutionary models with an infinity of locally and globally
interacting agents. Agents face repeated discrete choice problems.
Their utility depends on the actions of some designat&nbsp more››

We consider Backward Stochastic Differential Equations (BSDE) with
generators that grow quadratically in the control variable. In a more
abstract setting, we first allow both the terminal condition and the
generator to depend on a vector parameter&nbsp more››

William Thurston conjectured over twenty years ago that every compact
hyperbolic 3-manifold whose boundary is a possibly empty union of tori
is virtually fibred, that is, has a finite cover which fibres over the
circle. If true, it provides a sign&nbsp more››

Let G be an abstract group. It is known that if every finitely
generated subgroup of G has an infinite cyclic quotient, then G is left
orderable. Using an idea of E.Ghys, we prove that the converse is true
for all amenable groups. (This generalize&nbsp more››